Two (probably) unstable macroeconomic equilibria

Some people argue about whether the macroeconomy is inherently stable or unstable. I don't think that's a very useful question. Because.....it depends. And one of the things it depends on is monetary policy. And that is a useful discussion to have, because we can actually do something about monetary policy.

Don't adopt a monetary policy that would make an equilibrium unstable. Because if you miss that equilibrium by even the tiniest amount (which you almost certainly will) the economy will move further and further away from equilibrium.

I thank Steve Keen for (inadvertently) reminding me to do something that George Selgin had wanted economists like me to do. It's not often any of us get the chance to write a post that will make both Steve and George happy at the same time. (Well, Steve should be happy, because I'm talking about unstable equilibria, but you never can tell.)

There's nothing new here. Just the old stuff, but perhaps told in a slightly different way.

1. Don't use monetary policy to target unemployment.

Targeting a real variable like unemployment sounds like a really good idea. Because it's real variables like the unemployment rate, and real income, that really matter to people. Much more than nominal variables like the price level, or inflation rate. So why not tell the central bank to target unemployment?

Like most economists, I think that if you loosen monetary policy then inflation goes up and unemployment goes down. At least, temporarily. There's some sort of short run trade-off. But I'm less sure about the long run. If you permanently loosen monetary policy, so that inflation is permanently higher, will unemployment go down, go up, or stay the same?

It is easy to build a theoretical model in which there is no long run trade-off. The Long Run Phillips Curve is vertical. Now any macroeconomist with any ingenuity could tweak that model to make the Long Run Phillips Curve slope in either direction. But I wouldn't trust those tweaks in either direction. The data don't help much either. When I look at the data, I think I see that countries with high average inflation tend to have high average unemployment rates. Which means the Long Run Phillips Curve slopes the "wrong" way. But I don't totally trust my lying eyes. Because it might just be that screwed up countries tend to get everything wrong, and it's not that their loose monetary policy is causing high inflation and high unemployment. It might just be something else that is screwed up in those countries, that is causing both the high unemployment and the loose monetary policy.

But if you want monetary policy to target unemployment, you had better be very confident that the Long Run Phillips Curve slopes the "right" way. Because if it slopes the wrong way, you have got an unstable equilibrium. If you miss the equilibrium by just the tiniest bit, and set a slightly too low target for the unemployment rate, you loosen monetary policy to bring unemployment down, inflation will rise, the unemployment rate will eventually rise too, so you loosen monetary policy further, and so on, getting further and further way from the equilibrium (assuming it even exists).

Even if the Long Run Phillips Curve does slope the right way, and a stable equilibrium exists, it might be very different from what regular folk might think of as stable. A Russian doll is stable, but it sways back and forth a lot in a gusty wind. If the Long Run Phillips Curve slopes the "right" way, but is very steep, small shifts in the Phillips Curve will cause very big fluctuations in inflation if you target unemployment.

Most economists say the Long Run Phillips Curve is vertical, and so monetary policy can't target unemployment in the long run. They don't really mean that. They mean they don't really know which way it slopes, and vertical is probably a good approximation. And they don't want monetary policy to target unemployment, because the risk of the equilibrium being unstable, even if it exists, is far too high for comfort. And even if it is technically stable, it will move around a lot, so it won't look "stable" in the ordinary sense of the word.

As older readers will remember, targeting unemployment has been tried before. And it took a couple of decades to recover from the experiment and get both inflation and unemployment back down again.

Lets not go there again. It's a really bad idea.

2. Don't use monetary policy to target a nominal interest rate.

But that's what the Bank of Canada does, isn't it? Well, yes and no. Mostly no. What the Bank of Canada does is target 2% inflation. It only targets a nominal interest rate for a very short time period, of about 6 weeks. Every 6 weeks it adjusts the interest rate target, as needed, to try to keep inflation at the 2% target.

There (probably) exists a time-path for the nominal rate of interest that is compatible with an equilibrium in which inflation stays at (roughly) 2%. But:

We don't know what it is. It won't be a constant. And, most importantly, it will (almost certainly) be an unstable equilibrium. If we miss that equilibrium, by even the smallest amount, the economy will move further and further away from the equilibrium.

Suppose the central bank sets the rate of interest too low. Demand will be too high, and inflation will start to rise, and keep on rising.

It gets worse. As inflation rises, expected inflation rises too, the real interest rate falls for any given nominal rate, and so demand increases still further.

None of this is news to New Keynesian macroeconomists. They know you will get an unstable equilibrium if the central bank holds the nominal interest rate constant. So they insist that the central bank must adjust the nominal interest rate quickly enough and by a large enough amount to try to turn an unstable equilibrium into a stable equilibrium. And if people are confident that they can and will do this, expected inflation will stay anchored at the 2% target, which helps prevent one of the destabilising forces.

Whether that feedback rule for the nominal interest rate will always operate quickly enough and strongly enough and be credible enough to convert an unstable equilibrium into a stable equilibrium.....is another question. The answer looks a lot different at the Zero Lower Bound than it did before. Maybe it's time to stop using even very short term interest rate targets?

Comments

[George Selgin]

Yippee! I mean, thanks, Nick.

[Nick Rowe]

Thanks George. You were quite right to say we should say this. I hope Steve likes it too.

[W. Peden]

Nick Rowe,

Does it ever depress you that your post, which I imagine will surprise all too many people, is basically a very good summary of Milton Friedman's "The Role of Monetary Policy" (except with the order of interest rates and unemployment reversed) now over 44 years old?

If unstable equilibria don't occupy the mind of mainstream economists, then presumably mainstream economists must think that Friedman '68 is a very weird paper. Actually, given the (total?) lack of maths in Friedman '68 & the fact that it was in the AEA, it SHOULD be a bit weird for those only familiar with the modern AEA.

Milton Friedman: heterodox economist?

[Martin]

Hey Nick, so what I read above is that implicitly the real economy, the barter economy, is really really stable: you need to push really really hard and keep on pushing to change a real variable to keep it where it us until it breaks.

The unemployment rate is quite real; the nominal interest rate (i) is part real (r), and part nominal (pi) or i ~= r + pi. The lesson is: don't touch those real variables?

[Nick Rowe]

W Peden. Well, it might depress me. But then I think of the Carleton University motto: "Ours the task eternal", which provides solace. There will always be jobs for teachers.

The only case that comes to my mind where a "mainstream" (though, not really mainstream) economist forgot about the unstable equilibrium stuff that's clear in Friedman '68 was the infamous Kocherlakota episode. (And he has so much improved recently, it proves there's always reason to hope).

It's usually an implicit understanding. We don't talk about it much, because we know not to go there.

Martin: maybe. But a barter economy would be so very different in so many ways, even if you did assume some hypothetical zero transactions cost economy. But you could still get instability in a barter economy. If people had really stupid expectations (they might), or if fiscal policy were really stupid. Possibly other cases too.

But yes, the main lesson is indeed; don't use a nominal variable (monetary policy) to try to target a real variable. (Interest rates are actually a bit weird, on the nominal/real distinction. Because all interest rates, both nominal and real, have the units 1/time. And 1/time is real units. True nominal variables have $ in the units. I got my head around this once, but now I have forgotten what I figured out.)

[Martin]

Yes, you're right about barter. I first read you as a bit of Wicksell, but then I instinctively switched back to Walras + Money with non-neutrality in the short run, and neutrality in the longer run.

Hence why I thought of barter; I have this incessant need of fitting square pegs into round holes. And from your response, I am guessing that I am wrong to read you as simply Walras + money?

[Nick Rowe]

Don Patinkin's Money Interest and prices is about as close as you can get to Walras + money. You could do a lot worse than walras + money. But I don't think it's really me.

[K]

Nick,

Bog standard NK economics right until the penultimate sentence. But "Maybe it's time to stop using even very short term interest rate targets?" is a non-sequitur. I've been reading you for long enough to know what you're probably on about, but still... what are you on about?

[Nick Rowe]

K: I thought it was a sequitur myself? Ditch the short term interest rate target, and replace it with something with $ in the units. NGDP futures market, TSX-300 index, commodity bundle futures index? Dunno.

[rsj]

Ditch the short term interest rate target, and replace it with something with $ in the units.

So, we should close the discount window and shutdown Fedwire? Just walk away from helping banks cover intra-day and overnight funding shortfalls? Let the free market do it?

If we don't, then how much do we charge banks who are short of short term funds? And isn't that our target?

[Nick Rowe]

rsj: it would probably be best to keep the discount window open at a floating penalty rate for the lender of last resort function.

[rsj]

Nick,

How is that rate determined? If it is floating, then what other metric sets it?

[Nick Rowe]

rsj: you want me to convert Bagehot into some simple formula? Other people could give a better answer to that question than I could. Some rate, such that banks would never use it to any significant extent, if at all, in normal times, but would use it freely in a crisis. Perhaps no such formula can be found, because the lender of last resort function is inherently a judgement call, if risk is involved, which it is.

[K]

Not to interfere with rsj's line of questioning (which I think is sensible)... lets say the cb stops interfering with the market for reserves (you'd have to have a perfect settlement process every night) . Now you no longer have an instrument for the cb to effect policy. So it's just another loud mouthed think tank. Targets are great, but Chuck needs weapons. The interbank rate is a weapon, an NGDP futures *instrument* could be a weapon. An NGDP target is not a weapon. Chuck must say how he intends to use his weapons in order to effect his targets.

[rsj]

Some rate, such that banks would never use it to any significant extent, if at all, in normal times, but would use it freely in a crisis

Nick, it doesn't work like that. We have a credit based money system in part because are allowed to lend first and obtain reserves later.

Now, I understand that you do not believe that, that banks need reserves prior to lending, etc. But in our world, there is a payment system in which the CB, as a matter of course, lends billions of dollars per hour to the banking system in order to keep this whole thing working. These are not overnight loans, or emergency loans that we can spend a lot of time thinking about, but instantaneous intra-day loans necessary to keep everything working.

And banks need to know how much they will be charged in order to conduct their normal affairs and keep this credit-based demand-determined endogenous-money game going.

[rsj]

See, for example, http://www.newyorkfed.org/research/epr/08v14n2/0809bech.pdf

[Nick Rowe]

K: central banks can buy and sell government bonds, or gold, or other financial assets. Buying and selling very short term IOUs from commercial banks (overnight lending) isn't the only thing they can do.

rsj: the commercial banks settle their own daily transactions on the books of the Bank of Canada, and the whole balance nets to approximately zero every night. Nearly all overnight lending is between the banks themselves. Let that rate float. Target something else. We haven't always done it this way. We don't always have to do it this way.

[Nick Rowe]

rsj: "Now, I understand that you do not believe that, that banks need reserves prior to lending, etc."

No, you don't understand that.

[K]

rsj,

If the system settles perfectly, as it does in Canada most every night, no bank ends up with a net reserve position overnight. So there is no cost of reserves. (The fact that the interbank policy rate still is the anchor for all rates in the economy is critical, but the mechanism unfortunately is really badly understood by most macro economists). The point is I don't think Nick needs to buy into the nitty-gritty facts of the existing monetary system. But he does need to propose some policy under which the CB proposes to exchange/lend its reserves/currency and he needs to tell us the basic rules of the settlements process as he envisions it. Without that the CB really is nothing but yet another think tank.

[K]

Let me clarify: "no bank ends up with a net reserve position *with the Bank of Canada* overnight". Of course, banks have reserve debits and credits between them.

[K]

Nick: "central banks can buy and sell government bonds, or gold, or other financial assets."

Agreed. But if they do that they have to have a policy on IOR. If that policy is IOR=0, then the interbank rate will be zero.

[Determinant]

The details of how the Large-Value Transfer System works, which is what Nick and K are talking about, can be found in a detailed pdf-format book on the Bank of Canada's website.

Quick and dirty: The Bank of Canada sets a target Overnight Lending Rate and a target Overnight Deposit Rate. If the external borrowing rate is below the deposit rate, there is an instant, large and absurdly obvious arbitrage opportunity. The market will take advantage of that and the abnormality is corrected. The flip side is if the lending rate is below the general overnight market deposit rate; the settling banks will engage in a carry trade by borrowing from the Bank of Canada and depositing it in the overnight market until the abornormality is arbitraged away.

These arbitrage features are there by design, they are the teeth of monetary policy. It's simple, robust and you have to have a mighty large crisis to break the system.

The interbank overnight rate is the ultimate short rate, the risk-free rate. All other rates, for mortgages and GIC's, are based on this rate with additional basis points for additional term risk. In Canada mortgage "terms" are for six months to five years; the mortgage is rolled over many times under a conventional 25-year amortization. The amortization is not the term.

[rsj]

Nick,

You are basically saying that central banks should not be market makers for bank reserves. But that is the foremost role of central banks. It's why they are called reserve banks. And the market maker sets the price.

Banks are market makers for money for the non-financial sector. But banks themselves need a market maker for each other's liabilities. Historically, private reserve banks sprang up to play this role. But even then, the price of reserves reflected the plumbing -- e.g. shortages of reserves among certain banks -- and not economic conditions in the non-financial sector. This free banking era was financially volatile. To settle that volatility, we created government reserve banks that made markets in reserves. They advertised the price, and they served the banks that made markets to households.

Now, in a Walrassian model, there is a fairy that makes all markets simultaneously. The auctioneer announces the price. With such a fairy, there is no need for a central bank, but also no need for banks. And no need for money. So you create a fictional need for money by sticking it in the utility function, to balance the fiction of the global market maker, and that frees up reserve banks to do other things than make markets in reserves.

But in our world without fairies, central banks will always first and foremost make markets in reserves, meaning they will conduct policy by setting the price of reserves.

This is actually a great debate, because it completely captures the endless disputes about differences between reserves and deposits, about why there is a demand for deposits separate from a demand for reserves, and about why we need both banks to make markets in deposits as well as central banks to make markets in reserves.

And then there is the meta criticism that if you get the institutions wrong, your policy advise (e.g. stop making markets in reserves) will be all wrong.

[Nick Rowe]

Hmmmm. Why do I get the feeling that people don't want to talk about unstable equilibria?

[Lord]

Ooooo, those scary hyperinflation days of the 80s and 90s. Not that we should repeat the 70s but it isn't inflation that is scary but accelerating inflation in an environment unused to it. I have my doubts we want stable inflation though. Rather we may want an inflation that rises gently over the cycle destroying the debt created in the prior recession to make fighting the next recession easier and reduce the likelihood of a Minsky moment, then slowing inflation as real debt falls. Just a guess though.

[rsj]

Hmmmm. Why do I get the feeling that people don't want to talk about unstable equilibria?

We *are* talking about unstable equilibria by attacking the model. Attack the model and you attack the conclusion. Model's don't need to be perfect, but getting the basic and most important role of the central bank right is a requirement for a model that tries to predict the effects of CB policies, no?

But if you want to talk about unstable equilibrium, let's talk about the greatdestabilization when we dropped the ball on fiscal policy and focused solely on monetary policy to stabilize aggregate demand. The consequences of this policy were much more devastating on a global GDP loss or global employment loss basis than the stagflation period at the end of the previous regime. It's an order of magnitude worse blow up, so I'm not sure how you can argue that one form of policy is stable and the other is not. Canada has sailed by relatively well, but let's see how well it does when the housing bubble bursts.

If you want to talk about unstable equilibria, then explain why you need to cut rates by more to speed up the economy than you need to raise rates to slow it down by an equivalent amount. How is that a stable equilibrium? How are stagnant wages and a growing compensation/productivity gap stable? How is an economy based on asset price appreciation stable?

I will take some inflation instability any day, provided that male long term unemployment falls to the level that it was during the bad old years of stagflation, or that we get some stability in median wage shares.

[rsj]

Sorry about the typos. Those links should be separated by a space. And the contraction. Ugh, it's late here. I will resume battle tomorrow!

[Ritwik]

Nick

I think that NAIRU and the Wicksellian natural rate are both good definitions of macroeconomic equilibrium (in a Keynesian-Wicksellian sense, they're perhaps isomorphic) and that it may be difficult, if not impossible for a monetary authority to hit either of them. I think that targeting the NAIRU equlibrium is unstable because while targeting the Wicksellian one is simply difficult, not unstable. While I'm not in favour of targeting asset markets, I think an NGDP target makes a lot of sense, esp. if you happen to choose one which is sufficiently above 0%, sufficiently above the typical 'natural' short rate and sufficiently below the typical 'natural' cost of capital. 5% is a good first approximation.

How to go about targeting the 5%? I'm not quite sure. I would probably recommend some combination of IoR and helicopter drops/ mop-ups in a way that responds to 'the forecast'. How to develop the forecast? Again I'm not quite sure. But there cold be several ways, including simply taking a poll. But in general, I'd not target asset markets.

To K's and rsj's line of questioning, you're actually quite safe. Monetary policy and liquidity policy are separable. ffr = ior + svr (scarcity value of reserves). Even if you conceive of monetary policy as setting 'the' interest rate, this is the ior and setting this can be taken out of the central bank (even if it is the central bank that pays the interest and holds the reserves). An open market committee could do it. The repo market could do it.

The channel in which the ffr operates - the bounds of svr given by 0 and the discount window rate - is then free to be set by the lender of last resort/ discount window operator. The authority that sets the svr has the narrower view of financial stability and the payments system. It does not need to bother itself with hitting macroeconomic inter-temporal sweet spots.

The monopoly issuer of reserves and the decipherer of the numeraire rate of the economy do not need to be the same. The monopoly issuer only controls svr. The Friedman rule sets svr equal to zero, but for financial stability and 'liquidity as a put option' reasons, this marginal cost pricing of reserves need not be followed. In systems where the ior traditionally been 0, the analysis has been confused because it looks like the ffr = svr but given how most of these systems operate at 'peak liquidity' it's better to look at them as ffr = ior and the svr = 0.

Lest anyone think I'm talking crazy stuff, I'm basically invoking Charles Goodhart (and Willem Buiter) nearly idea for idea.

[Ralph Musgrave]

Monetary policy is bonkers. Period. Full stop. At least its nonsensical to use it without corresponding fiscal measures, and for the following reasons.

1. It’s distortionary. That is boosting an economy just via interest rates (i.e. borrowing) makes as much sense as boosting an economy just via people with brown hair.
2. QE benefits the rich far more than the poor.
3. The idea that there is a relationship between interest rates and the actual availability of credit is a joke.
4. Low interest rates promote bubbles.
5. At the start of a recession, extra borrowing and investment is exactly what is NOT NEEDED because there is a surplus of unused capital equipment.
6. The effectiveness of interest rate adjustments is hindered by movements of foreign currency into and out of the relevant country, e.g. high interest rates designed to damp demand attracts foreign hot money, which negates the intended effect.
7. Prior to the crunch people were borrowing like crazy to fund property speculation. In a free market, interest rates would have risen which would have choked off some of the speculation. But central banks in their infinite stupidity use interest rates to control inflation, and inflation wasn’t too bad prior to the crunch because the extra resources going to speculation were resources REMOVED FROM elsewhere. Net effect on inflation was almost nil.
I.e. using interest rates of regulate economies is a stroke of genius, I don’t think.

[JKH]

“Let that rate float”

The CB determines the amount of reserve balances through its own balance sheet management. And unless it deliberately sets the price of reserves, the overnight interest rate will either be zero (reserves in excess of system settlement requirements, causing banks to drive the rate to zero through competition to invest excess funds in things like treasury bills), or potentially unlimited on the upside (reserves short of system settlement requirements).

In the latter case, there has to be a rule and a pricing for overdrafts (i.e. overnight loans from the central bank), since at least one bank is short of funds by assumption. Otherwise, there is no system at all – it just collapses into chaos, because there is no pricing for settlement funds, and there is no pricing discipline motivating a system settlement process that intends to avoid more expensive central bank funding in the normal course.

Administered pricing of reserve balances is a necessary consequence of the institutional design of the system, with commercial banks settling on the books of the central bank.

So there must be pricing of settlement funds and the central bank must set it. And so the central bank sets the interest rate. It has to. It has no choice.

(The only realistic example I’ve seen so far without this is the case of a currency board, but this is an intricately interlinked FX dependent system rather than a true domestic currency settlement system. Maybe somebody can point out others.)

BTW, it seems to me that market monetarists (including Sumner) who complain that the Fed caused the recession by allowing NGDP to fall and by keeping money "too tight" describe that tightness as a failure to lower the policy rate quickly enough. So they are rate focused in that context. I think your use of the term “target” to describe a potential central bank “interest rate target” is confusing, suggesting a false choice. Market monetarists would be admitting the co-existence of two targets in this case (the interest rate and NGDP), although in different modes, because they acknowledge that the Fed set the rate on the way down to zero, in their argument favoring an NGDP targeting antidote.

[JKH]

In other words, treasury bills trade at the rate they do because the Fed sets the policy rate where it does (with the spread adjusted for all sorts of complicating institutional frictions), and it can't be any other way. It certainly can't be vice versa.

BTW, Volcker still set the funds rate - because in responding to money supply figures, he still had to make the decision on where to stop it out on the upside - which he made though active choices on reserve management and the effect of reserves on funds pricing. Just because he didn't announce a rate doesn't mean he didn't determine it by central bank actions in reserve management. It was not a market determined rate in that sense. It required judgement in translating money supply outcomes to appropriate reserve and reserve pricing settings. (And the discount window rate was a known, central bank determined number).

[JKH]

Nick, didn't you do a post on a gold rule for interest rates, along these lines?

[JKH]

Nick,

There’s something strange about the way you’re flirting with the use of the term “targeting” to apply to what the central bank does with its policy rate. This is the catalyst for a false choice. It’s not a choice between the policy rate and NGDP, or between the policy rate and money supply, or between the policy rate and gold. It’s a choice between things like CPI, NGDP, money supply, and gold. Volcker chose money supply. You choose NGDP. Bernanke now chooses a history dependent employment path, apparently constrained by inflation in some important way. But every one of these requires that the central bank sets the policy rate in response to those things. And using the term “targeting” to describe this just muddies the waters.

[Nick Rowe]

JKH: "And using the term “targeting” to describe this just muddies the waters."

I agree the terminology is muddying. But the Bank of Canada uses the same word to talk about its "inflation target" and its "target for the overnight rate". The key distinction is that the latter is a temporary conditional target that is changed, as needed, to try to hit the former, longer term, unconditional target. In the olden days we would sometimes talk about "intermediate targets" to describe a temporary conditional target. But if I said that the overnight rate is the Bank's "intermediate target" (which it is in a sense) people would get even more confused, and say "no it isn't; it's the instrument" (which isn't strictly correct).

That's why I said "But that's [target the rate of interest] what the Bank of Canada does, isn't it? Well, yes and no. Mostly no."

The main position I am attacking in the post is someone who says "The Bank of Canada should "set" the rate of interest at (say) 4% and keep it there for decades". Only at the very end of the post do I raise the question: well if decades is too long, is even 6 weeks too long? (But it's not really the length of time per se; it's more the conditional/unconditional aspect, and the role it plays in the communications strategy, that matters.

[Nick Rowe]

JKH: "Nick, didn't you do a post on a gold rule for interest rates, along these lines?"

I can't remember. I think I have touched on it a few times, in the past. I seem to remember a dream about a girl with golden eyes. It's really just Irving Fisher's old "Compensated dollar Plan". The central bank adjusts the price at which it will buy and sell gold, in order to keep the Price level (in Irving Fisher's case, but it could be NGDP or whatever) on target, and lets the market set interest rates.

Ralph: "I.e. using interest rates of regulate economies is a stroke of genius, I don’t think."

So, you agree with me?

But you really do need to get out of the head-space (sorry for the hippy-talk) of thinking that monetary policy is is is interest rates. It isn't. And it could be even less about interest rates than it is now. Instead of the central bank trying to set interest rates where desired saving = desired investment, and changing them every 6 weeks if it thinks desired S or I has changed, it could do something else, and let the market adjust interest rates up or down.

[JKH]

Nick,

“The main position I am attacking in the post is someone who says "The Bank of Canada should "set" the rate of interest at (say) 4% and keep it there for decades".”

Good grief. Does anybody actually think that way? That can’t be the issue, surely.

Sorry, I really wasn’t clear in my language that seemed to criticize your language, and that shouldn't be the criticism exactly.

It’s not so much the double use of “target”, but the question of “setting” the rate that’s at the heart of this.

And whether it’s 6 weeks, or indeterminate (it used to be) or unannounced (it used to be) also is not the issue.

The way to think about it IMO is to use a base case of a continuous time rate setting process, and layer those administrative arrangements over that. The continuous time response is then a function of what it “targets” in your sense of the example of NGDP as a target. I’d say gold, money, and the CPI are examples of alternative targets in this sense.

My point is that the central bank ALWAYS sets the rate as a functional dependence on whatever targeting process is in place as above. It MUST do this, given the institutional mechanism of how the commercial banking system clears on the books of the central bank and uses settlement balances (or “reserves”) to do this.

I really think you monetarists miss the entire point that your pure economic model way of thinking about things actually depends on the fact that you almost always assume this institutional arrangement in your description of the world. Therefore, you should recognize how it works explicitly as a constraint on your modeling.

I suppose you can model the world in a barter system or a system with no commercial banks and no clearing system and no pricing of settlement balances in that system, but that is another world – perhaps useful for illustration, but essential that you distinguish it that way. As soon as you assume banks clear through a central bank, that all changes. Pricing changes – because banks are motivated to price all their assets and liabilities according to signals given by the reserve setting and reserve pricing at the margin.

BTW – I think the Krugman/Keen debate was all tied up in this. I had a look at two of the Brainard papers going back, which was PK’s base of reference, and it’s very interesting that the commercial bank reserve clearing system (and commercial banks altogether) are entirely omitted from those papers. And I think that’s where Krugman went off the rails in his notion that banks don’t complicate the issue at all – it’s easy to say that when the original paper doesn’t even include banks.

[K]

Nick,

If we are going to talk about instability (I'd like to) I don't see how we can escape introducing a model (preferably a toy model) of fractional reserve banking. We need to talk about what (if anything) the CB *has* to do in an ideal world. If you see a mechanism whereby the CB can buy assets using its liabilities, but can avoid determining the short rate on its liabilities, maybe that would be a good starting point for a toy model.

I'm sure people will object that institutional details matter. That's fine, and to the extent that they do, we should start with a simple model, see how the dynamics play out, and then add complexity and see if it makes any difference. Without a common framework model, we are just going to get bogged down in the same old arguments, each person having her own mental model, and everyone talking past each other.

[Nick Rowe]

Ritwik: "I think that targeting the NAIRU equlibrium is unstable because while targeting the Wicksellian one is simply difficult, not unstable."

Hmmm. Why do you think that? If it weren't for the distinction between real and nominal interest rates (i.e. if the central bank were targeting a real interest rate on indexed bonds) I would say the two would be isomorphic. But if it targets a nominal interest rate, I would say it must be much more likely (almost certain, i.e. except in a really weird model) to be unstable. Because you have that additional positive feedback channel from inflation to expected inflation to a lower real interest rate.

Very interesting stuff on Goodhart and Buiter. I haven't read them on this (unless I've forgotten), but I'm thinking along those sort of lines. You could even separate central banking into three jobs: running the payments system (and you could *maybe* make an analogy there to a dealer in the stock or bond market, who quotes buying and selling prices and keeps a small float and adjusts those prices continuously); acting as lender of last resort in a crisis (much more of a judgement call; and doing monetary policy (via say OMOs or gold or whatever purchases).

I know there has been some (very little) discussion (e.g. between my late colleague TK Rymes and David Longworth, ex-BoC, IIRC) of what would happen if the Large Value Transfer System were run by the commercial banks themselves with the Bank of Canada staying out of it.

[Nick Rowe]

rsj: "If you want to talk about unstable equilibria, then explain why you need to cut rates by more to speed up the economy than you need to raise rates to slow it down by an equivalent amount."

You are asking me to explain a "fact" that I don't think is a fact. And the fact that interest rates have been falling over time doesn't make that thing a fact.

(I thought you MMT guys wanted 0% interest rates, anyway? Or is that just some of them? ;-) )

[Nick Rowe]

JKH: "Nick,

“The main position I am attacking in the post is someone who says "The Bank of Canada should "set" the rate of interest at (say) 4% and keep it there for decades".”

Good grief. Does anybody actually think that way? That can’t be the issue, surely."

I *thought* some of the MMT guys were saying that (only it was 0% not 4%). Maybe I totally misunderstood them?

And what is Ralph Musgrave saying above, if he doesn't like central banks moving interest rates up and down because that's putting the burden of adjustment on people who are interest-sensitive?

I mean it would be nice if I were only attacking an imaginary straw man here as a pedagogical thought-experiment. But am I?

[K]

Nick: "I *thought* some of the MMT guys were saying that (only it was 0% not 4%). Maybe I totally misunderstood them?"

Actually, I thought you were saying that. If you want to buy assets and you have zero IOR, then you are setting rates at zero (I think you might be a closet MMTer!) If, on the other hand, you want non-zero IOR, you are going to have to have a policy on that rate. And *that* policy matters.

[Nick Rowe]

K: Interest on reserves is a fairly recent policy. It used to be 0%. (I think it maybe is still 0% in some countries?). But interest rates were not 0% when interest on reserves was 0%.

[K]

Nick,

No, rates don't have to be zero just because IOR is zero. Depending on the efficiency of the clearing mechanism, banks may hold a small amount of excess reserves at IOR=0. In Canada, that small amount is generally exactly zero.

*But*!

The CB cannot introduce more reserves at their discretion in such a system. Lets say you are a bank and the CB buys $1Bn of T-bills from you. What are you going to do with that $1Bn of non-interest earning reserves? You are going to lend it at the interbank rate, right? Except, I (another bank) don't want it either. *Nobody* wants it because it's *excess*. The most I, or anybody else, will pay to borrow it, is whatever we can earn on it by holding it overnight. I.e. *zero*. Therefore the interbank funds rate drops to zero. You cannot control both excess reserves and the *difference* between the funds rate and IOR at the same time. If you want to control excess reserves you must have FF=IOR. And then you need a policy for FF. This has nothing to do with esoteric, particular institutional arrangements. It's inescapable economics of the clearing system.

[Nick Rowe]

JKH: "BTW – I think the Krugman/Keen debate was all tied up in this."

Yes and no. It's better to think of that as a short run/long run debate. PK was talking LR, and SK was talking SR. But SK's SR model (where the rate of interest is exogenous) doesn't make sense in the LR, precisely because the equilibrium is unstable (it's my second case above). And since (IIRC) the debate was about what caused the increase in the level of debt over a couple of decades or more (?), we definitely aren't talking about the SR where the rate of interest is exogenous. So SK's explanation doesn't make sense over that sort of time-scale. And PK's objection is perfectly valid in the LR.

The Brainard/Tobin stuff, even though PK brought it up, wasn't really relevant to the debate, IMHO.

[Alex Godofsky]

@K:

What if the central bank is just fine with interest rates plummeting to zero in response to the monetary injection?

What if the central bank just out-and-out tells everyone that the $1Bn T-bill purchase is permanent. The money is there, y'all have to figure out what to do with it.

Would it make sense that eventually desired bank lending might rise enough that the excess reserves become required reserves, and then interest rates would return to a positive value?

Would it make sense if interest rates plummeting to zero actually sped up that process?

[K]

Alex Godofsky,

Yes it makes sense. But the quantity of excess reserves is *utterly* irrelevant. The only thing that has any relevance whatsoever, is the *time* at which excess reserves will be allowed to return to zero, i.e. the time at which the short rate will be allowed to rise above zero. And after that, the only thing that matters is the short rate (excess reserves will be zero). And since the quantity of reserves is irrelevant before the rate hike, the only thing that matters in that period is the fact that the short rate is *zero*. From which we can conclude that the only thing that matters *at every point in time* is the value of the short rate. The path of the quantity of excess reserves is either

a) irrelevant (when r=0); or
b) informationless (i.e. 0) when r>0

[Nick Rowe]

JKH: ironically (actually, it's more funny than ironic) my own "very short run" analysis, when I'm yammering on about banks creating hot potatoes and planned expenditure being greater than expected income, is actually *much* closer (at least in spirit) to Steve Keen (AFAIK) than it is to something like Tobin or the official New Keynesian story.

[K]

Alex Godofsky: "What if the central bank just out-and-out tells everyone that the $1Bn T-bill purchase is permanent. The money is there, y'all have to figure out what to do with it."

Actually, *that* part of what you said doesn't make sense. The existence of $1Bn of reserves has no impact on the behaviour of any bank. They simply don't care. It costs them nothing, and it earns nothing. So they don't have to figure out anything. They know the CB will buy it back in time to start raising rates again. (Or the CB will institute IOR=FF (a floor system) and the banks will never have to care about the quantity of excess reserves.)

Nick: "Steve Keen"

There you go. I knew you were an MMTer.

[Alex Godofsk]

@K:

Even when r=0 doesn't the quantity of excess reserves matter in that it gives us some idea of when r>0 will happen?

Let's hypothesize a central bank that completely ignores interest rates and conducts monetary policy purely through setting the total quantity of reserves. Every six weeks they meet and decide on a new quantity. They pick the quantity that they think is most consistent with their NGDP level target (or inflation target, or price level target, or whatever).

Why, exactly, wouldn't such a central bank work? At some points maybe r=0 for extended periods, so what they are doing is pointless in the short term, but since their policy would, in your model, very definitely determine the path of interest rates, why wouldn't it be able to do all the things that the current interest rate-targeting central bank can do?

[Alex Godofsky]

(sorry, I cross-posted before)

@K:
Actually, *that* part of what you said doesn't make sense. The existence of $1Bn of reserves has no impact on the behaviour of any bank. They simply don't care. It costs them nothing, and it earns nothing. So they don't have to figure out anything. They know the CB will buy it back in time to start raising rates again. (Or the CB will institute IOR=FF (a floor system) and the banks will never have to care about the quantity of excess reserves.)

Eventually won't someone at the bank say "we've got a billion dollars sitting here earning us nothing. Why don't we buy some stocks with it?" ?

[Alex Godofsky]

Actually, I had an even better idea. Why not pay the money out as dividends to shareholders? If I held shares in a bank that was sitting on a billion dollars that were doing absolutely nothing for me, I'd be happy if they just handed me my share of it. I'd go buy some ice cream.

[JKH]

Nick,

“But SK's SR model (where the rate of interest is exogenous) doesn't make sense in the LR, precisely because the equilibrium is unstable (it's my second case above) ... actually *much* closer (at least in spirit) to Steve Keen (AFAIK) than it is to something like Tobin or the official New Keynesian story”

I’m sort of OK with all that. The way in which you describe the interest rate dynamic actually makes good sense to me, starting here:

“Suppose the central bank sets the rate of interest too low.”

BTW, I should have said I like both unstable equilibrium examples of your post, including the case of the central bank setting the policy rate and undershooting or overshooting, in recurring fashion, and in response to what the long term path “needs” to be. But I think that path is a partial function of each short term response, which the central bank controls. And so the central bank is continuously supplying incremental exogenous inputs into what the path will eventually be. And as I said, the base case could be viewed as a continuously differentiable exogenous input in terms of the policy rate – frequency of administrative reset is just fine tuning (or not so fine tuning) of that base case.

Related but separate issue – one more general concept I’m having a great problem with is the notion that a “permanent increase in the monetary base” has some special significance in monetary theory or in market monetarist thinking. It’s actually just about the only thing in Woodford’s paper I found quite inconsistent with the rest of his thinking. Maybe another time for that – but whether or not this idea of permanence is important depends very much on how you view the importance of the base versus interest rates in the short run – and Woodford mostly makes the case that it isn’t, which I agree with. He’s a rate guy, not a base guy, in the short run; yet he refers to this permanence idea with a different emphasis. My own scepticism could be summarized as comparing an expanded monetary base (bank reserve balance component) as a forced injection of quasi-treasury bills directly into the asset portfolios of the banking system. It's a liquid asset - much more so than a medium of exchange - and the fact that the central bank forces this position onto the banking system means the banks will adjust their overall liquidity management strategies accordingly. That's what they're doing now, and that's what they'd do if it were permanent (e.g. they might sell actual bills they might otherwise hold - sell them into the non-bank sector, or avoid holding those bills and similar liquid asset compared to the counterfactual of no monetary base expansion). But the most important operational idea here is that banks do not "lend reserves" to non-banks; and reserves are not the criterion for banks taking on more risk via lending or asset acquisition, which they need to do to get the NGDP mechanism or any other mechanism moving. (Let me emphasize that this reserve idea is not "MMT stamped"; its the way the banking system works.)

[JKH]

Nick,

Do you ever think about the vertical Phillips curve as a near-zero bound for unemployment?

[K]

Alex,

"why wouldn't it be able to do all the things that the current interest
rate-targeting central bank can do?"

First of all, when *not* at the ZLB, you can't determine the short rate that way. The exact quantity of excess reserves depends critically on the microstructure of interbank settlements. On most days in Canada, the system achieves zero excess reserves, as it should if the process is efficient. On such a day, the interbank rate would be zero if IOR was zero and the BoC forced any excess reserves. In any system, the quantity of excess reserves (though *tiny* compared to any relevant quantity in the system) will fluctuate wildly due to particular settlement events. Lets say that on some day in 2007 there were $10Bn of excess reserves demanded in Fed Funds. The following day the Fed suddenly decides to fix excess reserves at $10Bn. But some bank for God-knows what reason decides to hold an extra $1Bn of reserves. Suddenly the rest of the banks cannot get their required liquidity for tonight. Since they *need* those reserves for whatever reason, the demand for Fed Funds will explode as will the FF rate. If, on the other hand, that bank had decided to hold $1Bn less of reserves, the FF rate would collapse to zero (or whatever IOR is). So no, it's not possible in any system, whether it's messy like Fed Funds, or nearly perfectly efficient like LVTS, to set the level of reserves. Demand on any given day is simply totally inelastic.

"Eventually won't someone at the bank say "we've got a billion dollars sitting here earning us nothing. Why don't we buy some stocks with it?" ?"

No. There is no difference to the bank between

a) Spending $1Bn of held excess reserves on stocks; and
b) Selling $1Bn of T-Bills and using the proceeds to buy stocks

So the bank's decision of moving from the risk free rate to stocks is unaffected by the decision of the CB to buy $1Bn of T-bills.

[Alex Godofsky]

@K:

A short objection - we aren't talking about fixing the quantity of excess reserves, but the quantity of total reserves.

So no, it's not possible in any system, whether it's messy like Fed Funds, or nearly perfectly efficient like LVTS, to set the level of reserves. Demand on any given day is simply totally inelastic.

IOW, the central bank would have to meet much more often than every 6 weeks (more like every 6 minutes) to keep the system functional? OK, that is a plausible story.

No. There is no difference to the bank between

a) Spending $1Bn of held excess reserves on stocks; and
b) Selling $1Bn of T-Bills and using the proceeds to buy stocks

So the bank's decision of moving from the risk free rate to stocks is unaffected by the decision of the CB to buy $1Bn of T-bills.

That's only after the rate has collapsed to zero. Let's say r>0 and the economy is puttering along just fine. Then Ben Bernanke decides to buy $1Bn in T-Bills. The story you tell is:

1) This makes r=0.
2) Now that r=0, the bank is indifferent between holding $ and T-Bills.
3) Since the bank didn't sell the T-Bills to buy stocks earlier it won't sell the dollars for stocks now.

But the bank had only chosen to hold that quantity of T-Bills when r>0! Now r=0 and we can't take their previous portfolio allocation for granted. Maybe r=0.05 before, and the were perfectly happy to hold T-Bills given them a nice return. Now those T-Bills have been replaced with money at r=0, and they can't find any T-Bills to buy at r=0.05. So now they go out and look at other assets to buy, like corporate bonds or stocks, which are still providing a positive return.

[JKH]

Alex/K

"Even when r=0 doesn't the quantity of excess reserves matter in that it gives us some idea of when r>0 will happen?"

Absolutely not. No correlation whatsoever.

Run the numbers. My estimate under any reasonable assumptions for US economic and financial system growth is that converting $ 1.7 trillion of excess reserves to required reserves in the US banking system would take a period of time that would approach the beginning of the 22nd century.

I suspect the fed funds target rate will be increased before then.

[JKH]

The ability to manage a non-zero policy rate without paying interest on reserves depends on the leeway the central bank has to provide excess reserves in a zone that covers only the elastic portion of the reserve demand function. Look at the historic pre-2008 excess reserve series for the Fed. That is a very narrow zone indeed, and extremely stable in its narrowness.

Anything outside of that is the unlimited zone in which the demand for reserve balances is perfectly inelastic. And interest must be paid on reserves at the support rate for the policy rate - whether that support rate is zero or non-zero.

[Alex Godofsky]

@JKH

I'm pretty sure everyone knows that the current $1.7 trillion of ERs is temporary. K and I were talking about a hypothetical $1Bn injection. That said, what if we did find out that the $1.7 trillion was permanent, i.e. the Fed would never, ever reduce the level of reserves below the current number? You don't think that would do anything?

[Alex Godofsky]

@JKH

What is the terrible thing that happens if you don't pay IOR? Just that r=0? What if we don't care?

[K]

Alex,

The normal variation of mandatory reserves in the US over even a short period is much greater than the quantity of excess reserves. And the "elastic" regime of excess reserves typically much smaller than the quantity of excess reserves, and *totally* unknown ahead of time. So

a) if you insist on targeting excess reserves, then you will indeed be adjusting your target at an extremely high, intra-day frequency. And worse: by adjusting your excess reserve "target" you are doing so to make sure that Fed Funds isn't erratically bouncing between 0 and infinity.  If you are sane, what you are doing is stabilizing the Fed Funds *rate* target! So targeting excess reserves in a IOR=0 world, with FF>0 is just plain nonsense.

b) Since mandatory reserves can change by more than the total amount of excess reserves on any given day, targeting total reserves is even less feasible.

As to your story about buying stocks: The reason the bank decides to buy stocks has nothing to do with the CB's decision to buy T-bills. Imagine they act in two stages: 1) lower the rate to zero, 2) buy $1Bn of T-bills. The bank makes the decision to buy stocks based on the first action. The second is irrelevant. The only thing that mattered was the lowering of the short rate.

[Alex Godofsky]

@K

Regarding variation in reserves:

I don't have firsthand knowledge of this, but are you sure these things are true? Wouldn't that imply that the size of the Fed's balance sheet changes drastically within each day? I thought that the size of the balance sheet was relatively stable, but may be misunderstanding something.

Regarding buying stocks:

In my story the Fed never talks about interest rates. It just goes ahead and buys $1Bn of T-Bills. You said that forces r=0, and I'm cool with that.

Presumably, at some point after they spend the $1Bn on stocks (draining all of the ERs), r>0 again. In fact, per your story it should happen pretty quickly. The Fed buys a bunch of T-Bills, ERs>0, r=0, the bank buys stocks, ERs=0, r>0 is what should happen. And the new r should be at least partly dependent on how many T-Bills the Fed bought in the first step. So it seems like the Fed printing money is actually doing something!

[K]

Alex,

Under normal conditions (e.g. 2007):

Mandatory reserves *in the US* are vastly greater than excess reserves. Mandatory reserves, which make up a significant portion of the Fed's balance sheet, are very stable. Variations in mandatory reserves are big compared to *excess* reserves. Yes, I'm sure. I think the typical quantity of excess reserves used to be around $10Bn.

"It seems like the Fed printing money is actually doing something!"

Yes. It's holding the funds rate at zero. Or you could just put the funds rate at zero.

[Alex Godofsky]

@K:

It's not just holding the funds rate at zero. It's also (if permanent) telling us when* the funds rate will stop being zero, and where the funds rate will go after it stops being zero.

*conditionally

And, of course, what if the monetary injection changes expectations of future NGDP, etc. such that in short order there is more demand for loans in the real economy? In that case, if we had already been at zero then the injection may reduce the time until we exit the ZLB.

[Nick Rowe]

JKH: The "doubling the monetary base" question is a good one because it is a thought-experiment with a simple answer. The price level will (eventually) double (in standard simple models), and it's a stable equilibrium. And the interest rate will (eventually) stay the same. We just can't ask the same question using interest rate language to ask the question.

"Do you ever think about the vertical Phillips curve as a near-zero bound for unemployment?"

A long run Phillips Curve that's vertical at 0% unemployment? All (overly-) simple macromodels look exactly like that. But we know the real world doesn't look like that. The LRPC may be (approximately) vertical, but not at 0% unemployment. It's vertical at some number bigger than 0%, that we call the "natural rate" (or NAIRU). It would take some very serious (non-monetary) policy changes to get it anywhere near 0%. And some of those "cures" would be worse than the disease.

[Ralph Musgrave]

Nick,

I’m all in favour of letting “the market adjust interest rates up or down”, as you put it. But there is a problem there (might be a big problem or a small one – I’m not sure). This is that under fractional reserve, private banks can to some extent just ignore demands for interest from depositors, and lend money into existence when they see credit worthy borrowers.

I suspect that it’s only under full reserve that one gets a rigorous “supply / demand” relationship between savers and borrowers.

I touch on this in a recent blog post (see item No 3 near the end, if you’re interested:

http://ralphanomics.blogspot.co.uk/2012/09/george-selgin-explains-how-private.html

BTW . . . “PBS” in that post means “private bank system”.

[K]

Alex

"If permanent" it's telling us that the Fed wont hike rates until the nominal economy has multiplied by half an order of magnitude. Then, "if permanent" it's telling us that rates will suddenly go to infinity. I.e. "if permanent," it's pure lunacy.

Assuming it's *not permanent* (surely), we'd have to guess they'll guide total reserves down to wherever mandatory reserves happen to be at the moment they want to raise rates. Since mandatory reserves are definitely *not* the target, that moment will come whenever, e.g. NGDP, is back on target. I.e. we'll raise rates above zero when NGDP is back on target *no matter what the level of mandatory reserves at that point in time.* The only things that actually matter in this whole process are 1) the level of rates and the timing of the exit from the ZLB, and 2) the level of the target (NGDP). Mandatory reserves go wherever they happen to go, and total reserves, well, *nobody* gives a hoot what happens to those, except to the extent that they have to be back in line with mandatory reserves (and the CB has to stop controlling them) in order to start hiking rates again. So we really need to shortcut all the chatter about the irrelevant path of reserves and just lay out the NGDP contingent path of the short rate.

Again, we hike rates from the ZLB when *NGDP* is where we want it *independent* of the path of mandatory reserves.

"What if the monetary injection changes expectations"

Why would it do that? It has *no* effect. If we are postulating magical powers, why could just as well imagine it *lowering* NGDP expectations.

[K]

Nick,

Why the aversion to proposing a model of possible CB actions that we can all agree on? Wouldn't it be better if we had a common framework so we don't get bogged down in the same old debates, each with our own hidden assumptions? I really think it would be worthwhile to come to a consensus on the basic mechanisms. I was hopeful that our debate (which appears to have ended at 9:58) and the subsequent debate with Alex Godofsky might have been a good start. Am I making some basic error of economics or monetary modeling?

(And I hope I didn't give offense by calling you an MMTer. It was definitely intended as a joke.)

[rsj]

Nick,

You are asking me to explain a "fact" that I don't think is a fact. And the fact that interest rates have been falling over time doesn't make that thing a fact.

OK, so when we look at the period of price stability accompanied a period of the CB needing to cut more than it raised, the latter is not a fact, but an accident, whereas the former is not an accident but rather proof that the policy always works?

In a recession, risk premia rise a lot. In a boom, risk premia fall, but they do not fall as much as they rise in the recession. The situation is asymmetric. But the relevant rate for investment is the sum of the risk premium and the policy rate.

If you rely on adjusting the risk free rate alone to overcome the short run investment shortfall in the private sector, you will need to cut more during the downturns than you hike during the booms.

IMO, it's a lot more stable to have government invest directly more or less to cover short term fluctuations, and rely on interest rate policy for longer term "drifts" in the natural rate. That to me is a lot more stable than setting yourself up to always drift towards the lower bound.

But again, maybe it was just a 20 year accident of history.

Or maybe it really is in accident that most of the world's industrialized economies are up against a zero bound, and that most of these economies have seen risk-free rates trend downwards towards this bound.

[Nick Rowe]

K: "(And I hope I didn't give offense by calling you an MMTer. It was definitely intended as a joke.)"

No offense taken. Understood as a joke. (And not that *terribly* offensive anyway, even if it weren't a joke! There are much worse things than MMTers in this world. They seem to be decent people, just with slightly weird views about money/macro!)

[Alex Godofsky]

@K:

Assuming it's *not permanent* (surely), we'd have to guess they'll guide total reserves down to wherever mandatory reserves happen to be at the moment they want to raise rates. Since mandatory reserves are definitely *not* the target, that moment will come whenever, e.g. NGDP, is back on target. I.e. we'll raise rates above zero when NGDP is back on target *no matter what the level of mandatory reserves at that point in time.*

You are begging the question. The entire hypothesis is, no, this central bank doesn't care about interest rates. At all. You can't tell me that this central bank will do something with rates because this hypothetical bank doesn't use interest rates.

You can't take a hypothetical about a permanent monetary injection and then say "well, assuming it isn't actually permanent, your prediction won't come true".

The only things that actually matter in this whole process are 1) the level of rates and the timing of the exit from the ZLB, and 2) the level of the target (NGDP). Mandatory reserves go wherever they happen to go, and total reserves, well, *nobody* gives a hoot what happens to those, except to the extent that they have to be back in line with mandatory reserves (and the CB has to stop controlling them) in order to start hiking rates again. So we really need to shortcut all the chatter about the irrelevant path of reserves and just lay out the NGDP contingent path of the short rate.

Why not the NGDP contingent path of the monetary base? If there is a one-to-one correspondence between the size of the monetary base and the short rate (modulo ZLB where the CB can just say that the current size of the monetary base represents the size we expect it to be at exit) then a central bank absolutely can conduct monetary policy without talking about interest rates.

[Min]

"Don't adopt a monetary policy that would make an equilibrium unstable."

Unless, OC, you are in a suboptimal equilibrium. ;)

Autopoiesis now!

[K]

Alex,

Fine. So they wont raise rates. Instead, they'll set the level of total reserves and the market determined short rate will fluctuate wildly between zero and infinity. Which will obviously be terrible. So they'll start changing the quantity of reserves "every 6 minutes" in order to achieve a sensible target for the short *rate*. I.e. they'll be setting rates.

As I said, you cannot keep a permanent level of reserves. You are forcing the (market determined) short rate to zero until a point in time in the future that is totally unknown right now and tied to the level of mandatory reserves. Then you are forcing the (market determined) short rate to infinity. I.e. you are breaking the interbank market and making it impossible for banks to obtain their mandatory reserves. There is no plausible way to set the quantity of reserves if the market determined interbank rate is greater than IOR. The idea that the CB might not care about the rate on interbank clearing balances is not practical. How do you propose to effect transfers between deposit accounts at different banks without a functioning interbank funds market?

Remember, mandatory reserves are hundreds of billions of dollars and can change by billions a day. The difference between a market interbank rate of zero and and market interbank rate of infinity is probably a few billion dollars at most. Right now the quantity of reserves is trillions. There is no conceivable way to keep a reserve level target and a functioning interbank market.

"If there is a one-to-one correspondence..."

Because on any given day in the future, what that correspondence will be is unknown today. Both the future level of mandatory reserves *and* the required level of excess liquidity on some future day is totally unknown. The only thing we do know is that we'll want the clearing rate to be some reasonable number. But we have absolutely zero idea, within an extremely wide margin, what exact level of reserves will be required to achieve that rate. That's why we stick to targeting the rate and not the quantity.

[Alex Godofsky]

@K:

Then, in Nick's language (I think), the answer to "why use interest rates as an intermediate target?" is that demand for base money is extremely unstable over short periods of time, so you can't adjust it fast enough to avoid severe monetary disequilibrium.

[Min]

Nick Rowe: "I seem to remember a dream about a girl with golden eyes."

Ooh! I had a dream about a girl with golden eyes.

And the next day I met her. :)

[Min]

Seriously, now.

Nick Rowe: "Don't use monetary policy to target unemployment."

Because an unemployment target leads to an unstable equilibrium, right? But suppose, like now in a number of countries, unemployment is too high, and recovery is slow. Then why not target the current unemployment figure? True, an unstable equilibrium might go the wrong way, but regression towards the mean is more likely, eh?

I think that this is a reductio ad absurdum. We don't really think that doing nothing will make the current situation unstable, do we? (Although, as we know, doing nothing can be better than some attempted remedies, making it a second best policy. ;)) Well, if there is some unemployment target (namely, the current level) that does not lead to an unstable equilibrium, then the proposition that using monetary policy to target unemployment leads to an unstable equilibrium is false.

[Ryan V]

Nick: (Interest rates are actually a bit weird, on the nominal/real distinction. Because all interest rates, both nominal and real, have the units 1/time. And 1/time is real units. True nominal variables have $ in the units. I got my head around this once, but now I have forgotten what I figured out.)

When we calculate the USD-CAD exchange rate, we don't cancel out the $'s, because USD is obviously a different unit from CAD. It's just a coincidence that they're both called "dollars" and written with $'s.

I think it's the same thing when we talk about 2012 dollars and 2013 dollars, only less obviously so. If there are 2013 dollars in the numerator and 2012 dollars in the denominator, they don't cancel out. So nominal interest rates really are nominal variables.

Real interest rates are nominal rates minus inflation, but that's equivalent to saying they have 2012 dollars in both the numerator and denominator. Those do cancel out, and you're left with real units of 1/time.

[Alex Godofsky]

Ryan: but if you take limit of the interest rate as you've defined it, the units do cancel.

[K]

Alex,

Agreed. It's both unstable and inelastic. But even if it weren't, there is nothing to be gained from targeting the money supply. The ability to greatly increase the supply at the ZLB, doesn't actually have any impact (except to the extent of portfolio balance effects resulting from the nature of the assets being purchased, which could be positive, zero, or negative), so mostly it just causes confusion and diverts attention from sensible policy that actually has the potential to work in a big way.

But I still don't think that really gets at the core reasons why it's bad to manipulate the money supply. The real issue is that reserves just don't have any material impact on the economy. Think of the CB changing the quantity of reserves by a few billion dollars. Assuming rates are around 5%, the cost of holding reserves changes by $100M or so. Clearly that can't impact the economy. Yet, such a tiny change in quantity comes with with a massive change in the short rate that would have a huge impact on the economy since it directly effects the rate on trillions of dollars of loans. So is it best to model the economy as controlled by the level of reserves in a way that the quantity is irrelevant *except* in the tiny region of a critical, mysterious threshold where the quantity of reserves happens to have a massive effect on interest rates, *or* should we think of it as controlled by the interest rate in a simple, well-conditioned manner?

The confusion, in some cases, might come from thinking that the monetary transmission mechanism has to do with the bank incurring costs of holding reserves as it expands loans/deposits. It doesn't. The policy rate is the marginal cost of funding for the bank because it's the rate for clearing settlements through Fed Wire. If a bank wants to participate in the clearing system (i.e. send and receive US dollar payments) it *must* accept to borrow and lend in the Fed controlled Fed Funds market. Therefore Fed Funds is the marginal cost of of providing risk-free demand deposits and loans (lines of credit).

[Nick Rowe]

Min: "Well, if there is some unemployment target (namely, the current level) that does not lead to an unstable equilibrium, then the proposition that using monetary policy to target unemployment leads to an unstable equilibrium is false."

You lost me there.

Draw a graph (I should have done this in the post). Put unemployment rate on the horizontal axis, and inflation rate on the vertical axis. Draw a vertical line "MP" to represent Monetary Policy under an unemployment rate target u*. Now draw a Long Run Phillips Curve "LRPC". If the two curves cross, there's an equilibrium where they cross. If the LRPC slopes up (the "wrong" way) that equilibrium is unstable. You might *want* to target u* unemployment, but if you try to do it, you will fail.

The current level of unemployment may or may not be a long run equilibrium, and even if it is a long run equilibrium, it may or may not be stable.

The ideal monetary policy would have: only one equilibrium; it would be a stable equilibrium; and it would be a good equilibrium (or, at least, no worse than any other stable equilibrium).

[Nick Rowe]

Alex: "Then, in Nick's language (I think), the answer to "why use interest rates as an intermediate target?" is that demand for base money is extremely unstable over short periods of time, so you can't adjust it fast enough to avoid severe monetary disequilibrium."

Yes, but I might say it slightly differently. It's not so much how quickly you can adjust something, but how quickly you get accurate information that tells you you need to adjust it. (And I would use the word "volatile", instead of "unstable", if I were being pedantic.)

[Nick Rowe]

Ryan V: That sounds to me like it might be the right way to think about it. I need to mull it over. (Alex: I'm not sure they do cancel in the limit. The inflation rate is still defined even in the limit as we approach continuous time.)

[K]

Nick,

"It's not so much how quickly you can adjust something, but how quickly you get accurate information that tells you you need to adjust it. (And I would use the word "volatile", instead of "unstable", if I were being pedantic.)"

OK. Can we use the Canadian system as a starting framework for how such an adjustment might work? From there we can adopt any changes you might want. I understand that using reserve quantity as an intermediate target might require some institutional/operational changes and I'm open to considering any fractional reserve settlement system you prefer. Should we set IOR=0, or keep it slightly below the policy rate? Also, does your model depend on the existence of hand-to-hand currency, or can we eliminate that for simplicity? And do we need to add required reserves or can we just stick with zero?

[Min]

Nick Rowe: "The current level of unemployment may or may not be a long run equilibrium, and even if it is a long run equilibrium, it may or may not be stable."

Sounds right to me. That is true, however, of any target. If what you are saying is that there may be no stable unemployment equilibrium, then why mention targets? There is no guarantee that any target will be a stable equilibrium. It does not follow that targeting unemployment is a fool's errand.

The human body, while alive, is not in a stable equilibrium. However, that does not mean that we should not have fitness or health goals.

[Alex Godofsky]

But I still don't think that really gets at the core reasons why it's bad to manipulate the money supply. The real issue is that reserves just don't have any material impact on the economy. Think of the CB changing the quantity of reserves by a few billion dollars. Assuming rates are around 5%, the cost of holding reserves changes by $100M or so. Clearly that can't impact the economy. Yet, such a tiny change in quantity comes with with a massive change in the short rate that would have a huge impact on the economy since it directly effects the rate on trillions of dollars of loans. So is it best to model the economy as controlled by the level of reserves in a way that the quantity is irrelevant *except* in the tiny region of a critical, mysterious threshold where the quantity of reserves happens to have a massive effect on interest rates, *or* should we think of it as controlled by the interest rate in a simple, well-conditioned manner?

I disagree that we should see massively macroeconomic fluctuations from small monetary injections*. If the Fed prints a billion dollars, in your model we should temporarily see the short rate go to zero, but we should very quickly see the ERs converted to required reserves via additional bank lending. This bank lending would be motivated by r=0. Then you would see the short rate settle at some very slightly smaller value.

In fact, if the banks new that the Fed were going to operate this way, I would expect them to have marginal bond or stock purchases "lined up" to be executed in case of an injection.

In other words, IS/LM.

*If enough contracts are pegged to the short rate in a way that makes those contracts dysfunctional if it fluctuates temporarily then maybe you could have problems, but I'm skeptical that this would be a major problem (especially since people would choose another index for their contracts if it were a big deal).

[Nick Rowe]

Min: You aren't getting what I'm saying. Please draw the picture. See where the MP and LRPC cross? That's an equilibrium. Draw the LRPC as downward-sloping, and it's a stable equilibrium. Draw the LRPC as upward sloping, and it's an unstable equilibrium.

Words suck; pictures rule.

[K]

Alex,

As discussed, it doesn't take much to create chaos in the funds market. Imagine that one big bank decides to sit on an extra couple billion of reserves one day. As the day draws to a close, other banks will begin to scramble to cover their positions. Don't forget, if you don't cover you're bankrupt. And in your world, there's no discount window. (Or if there is, you'll have to introduce a *policy rate*). As it becomes clear that there is a shortage of funds, banks will panic and refuse to lend, ie. the funds rate will go to infinity. Why would a big bank do such a thing? Maybe they need the extra liquidity. Maybe they are trying to squeeze the market, hoping to lend at extreme rates. Maybe they fear another player trying something like that. The risks are extremely asymmetrical, without the Fed disciplining the settlement process.

So I don't see your process of slowly rising rates. I see a ZLB followed by extremely erratic fluctuations between ZLB and total settlement failure.

I'll admit, there may be a different equilibrium, *very* far away from the current system, in which banks hold massive quantities of excess reserves in order to cover all foreseeable settlement contingencies without any resort to interbank lending. Perhaps something closer to 100% reserve banking. The rate equilibrium (to the extent that there is any lending) in such a system is some kind of equilibrium between 0% IOR and the fear of lending out too much of your excess reserves and therefore somehow being gamed into bankruptcy. That would certainly not be efficient, but perhaps an excellent way to for the CB to extract an enormous quantity of seignorage. An equilibrium governed by estimation of extreme tail risk is unlikely to be stable though. I think it would be prone to bubble (gradual reduction of reserves) and collapse. And all the while the Fed would be controlling the quantity of reserves *effectively* in order to keep the short rate stable. I really don't think this is the system Nick is contemplating (but perhaps we'll never know :-( )

Certainly 100% reserves would work, and I think it would be instructive to discuss the stability of such a system as a polar extreme of the Canadian 0% reserve system. How does the CB regulate a 100% reserve economy?

[rsj]

Alex,

An increase in bank lending need not result in an increase in required reserves.

In Canada, required reserves are set at $50 million and yet bank lending is not hampered by this.

[rsj]

Nick,

The issue is that your picture omits how the curves change in response to interest rate changes. For example, a rate cut means that everyone's assets increase in proportion to the quantity of assets that they already own. So as they will have different marginal propensities to consume and save, a rate cut that increases the value of everyone's assets by 10% will also cause the savings demand curve to shift.

Similarly, fiscal policies can cause these curves to shift.

So I am saying that if we adopt a posture in which the wealthy, who take delivery primarily of capital income, are taxed at a lower rate than those who take delivery of labor income, then is it sufficient to rely solely on interest rate cuts to maintain demand? Or will that lead to an economy of asset bubbles that trends towards the zero bound? Is such a policy itself unstable or not?

I am not saying use monetary policy to target employment. I am saying use fiscal policy to target demand as well as monetary policy, because with a bad fiscal policy, monetary policy is going to be long term unstable.

[rsj]

^^^^Oops,

required reserves are set at zero, but $50 million of aggregate reserves is provided, in order to smooth things out a bit.

[Alex Godofsky]

@K:

It's possible that my confusion here is just my ignorance of the modern banking system. I know that in the past we had fractional reserve banks and a nearly fixed quantity of base money (gold) and they didn't blow up. Why, exactly, can't the modern system survive something similar?

Related: I am actually starting to question your story about the short rate (that it goes to zero instantly if you if you add ERs). That would seem to be true if the only holders of T-Bills were banks, but I believe some non-negligible fraction are held by non-banks or even individuals. Shouldn't the existence of these prevent the rate from instantly going to zero or infinity?

[K]

Alex,

"I know that in the past..."

Sometimes they blew up, sometimes they didn't. I don't want to get dragged into a debate about the apparent empirical stability of some undefined historical system of banking. In fact, not particularly interested in any empirical debate over banking stability at all. Not that it doesn't matter, but it'll never end and it will all be disputable and it will settle nothing. I'm interested in the characteristics of model monetary systems which produce stability (or not) at the point of competitive equilibrium. That at least is a debate we have a hope of settling (in principle).

A quick answer, though, is that risk in the modern system is completely disconnected from the quantity of reserves. Modern bank risk is controlled on the liability side by requiring adequate subordination (equity capital), not by regulating assets (reserves). Reserve requirements pose literally no constraints on the activities of modern banks. Maybe they could, but it wouldn't be our "modern system."

"I'm actually starting to question your story about the short rate..."

Well, fine!

No, most t-bills aren't held by banks. I don't see the relevance. You be Alex bank, I'll be K Bank. Maybe Nick will play the Bank of Canada! Lets say Nick buys $1Bn of Canadian T-bills from a pension fund who happens to have an account at Alex Bank. So Nick sends $1Bn to Alex Bank via LVTS (Fed Wire for Canadians). Alex Bank credits the pension fund $1Bn in their deposit account. The T-bills are transferred to Nick. Since your assets are unchanged, Alex, this has no impact on your risk capital. And we don't have reserve requirements in Canada (see rsj above) so now you have $1Bn of excess reserves. Lets deviate from actual BoC policy and imagine IOR=0, since that's the case that's interesting to monetarists (otherwise we don't know what they mean by "hot potato"). The policy rate is 5%. Large savings deposits earn 4%. Your current position is costing you $1Bn*(4%-0%)/365=$100K per day. What are you going to do with your reserves?

[K]

" Since your assets are unchanged"

or rather... Since reserves have zero risk weighting for regulatory capital purposes...

[Alex Godofsky]

@K:

I'm also interested in what the pension fund does. Presumably they sold the T-Bills because they wanted the money for some reason - perhaps they need to make pension payments (though that isn't really the scale we need) or are just rebalancing their portfolio into more equities or commercial debt. So I wouldn't expect those deposits to just sit there at Alex Bank. And whoever the pension fund buys those equities from probably had some use of the money in mind too. And so on. Presumably while all of this is happening Alex Bank will want to keep some fraction of those reserves on hand because it's going to need them right away.

But, sure, eventually banks are going to try to exchange those reserves for T-Bills and bid down that price. But we aren't just going to buy T-Bills from other banks - we will buy them from from non-bank holders of T-Bills, too. In the process we will manufacture more and more deposits. Buying T-Bills from non-banks is basically just lending, after all. And even without required reserves, presumably bank demand for reserves is at least somewhat proportional to total deposits, so eventually we should have created enough deposits such that our demand for reserves matches the quantity supplied.

Also, while all this is going on the interest rate on T-Bills is depressed, which means at the margin we will make some additional risky loans. And those people holding deposits at 4% instead of T-Bills at 5% will also, at the margin, want to spend some of those deposits on newly-produced goods.

Where is the flaw in this story?

[K]

I heard the pension fund is bullish on Alex Bank and wants to roll out of T-bills into Alex Bank paper. Will you issue them $1Bn? Maybe we need an agent of the representative household (labour, consumer, business all in one). rsj?

Governor of the Bank of Canada? What do you say, Nick? :-)

[K]

Why is the tbill rate depressed? For the moment the policy rate is 5% as is the rate on tbills. I assumed the equilibrium rate on deposits was 1% below the policy rate for reasons of cost/liquidity. There is no incentive to spend more yet. We are assumed to start at equilibrium and we are still there until something changes for the representative household. So far the only thing that's changed is a switch from tbills into deposits (or bank paper). If anything, a tiny portfolio balance effect. If you want, we can just set the deposit rate equal to the policy rate. I don't think it makes any difference.

[Max]

"Certainly 100% reserves would work, and I think it would be instructive to discuss the stability of such a system as a polar extreme of the Canadian 0% reserve system. How does the CB regulate a 100% reserve economy?"

Assuming the CB is paying interest on reserves, I don't think it makes any difference.

If there's sufficient public debt to cover the deposits, a reserve requirement is a superior alternative to deposit insurance. But that's a microeconomic issue.

[rsj]

And those people holding deposits at 4% instead of T-Bills at 5% will also, at the margin, want to spend some of those deposits on newly-produced goods.

Where is the flaw in this story?

You start with equilibrium. Households are already holding the level of deposits that they want. They are already spending at the rate that they want, given the income coming in.

Now the CB buys some bills from households. In order to buy those bills, it has to (slightly) lower the yield -- it has to make an attractive bid. The household will sell its bills to the CB and buy bills issued by the bank. Why would the bank be willing to sell bills to households? For the same reason that the household is willing to sell bills to the CB -- Because the yield is slightly reduced.

As a result of central bank bond demand increasing:

-- households may want to consume more, meaning that household bond demand goes down
-- bank net bond supply goes up (banks want to borrow more)
-- non-financial firm bond demand goes down (e.g. firms borrow more)

And the question is, what is the new point where excess bond demand = 0. Which sector shifts the most?

Let's see, banks are levered 20 to 1. Households are not levered at all. Firms are not levered.

Who is more sensitive to a change in rates of these three groups? Banks! So the net result is that *almost* all of the change is borne by the banking system.

As government bond demand increases, bank bond demand goes up. It is as if the central bank is conducting an asset swap with the banking sector. There is very little bond demand change in the other sectors, because they are 20 times less sensitive to rate changes than the banking sector.

And what happens when the central bank conducts an asset swap with the banking sector? The banks were holding bills, which are sold to the central bank, and they are now holding excess reserves. Household deposits are (mostly) unchanged. Firm borrowing is (mostly) unchanged.

To repeat

Where is the flaw in this story?

Ignoring the banks, who absorb the change. There is very little new spending created as a result of the CB bill purchase, because the banks are much more interest sensitive than any other sector.

[rsj]

And again, I don't understand why people who understand Ricardian equivalence perfectly well -- whether they agree with it or not -- don't seem to understand that the private financial sector can undo any portfolio shifts of the central bank, just as the non-financial sector is capable, in principle, of undoing fiscal shifts by Treasury.

And if you were to compare the two sectors -- the private financial sector versus the private non-financial sector, and ask which of them is credit constrained, so that it cannot undo the shift, it is clearly the non-financial sector that is credit constrained and not the financial sector. The *job* of the central bank is to ensure that the private financial sector is not credit constrained. The job of the central bank is to make QE ineffective. That is the institutional mandate.

Yet people really prefer the QE medicine to the fiscal medicine. Odd.

[rsj]

But I disagree with K about deposits paying the risk free rate. It is the fact that the non-financial sector is credit constrained while the financial sector is not that is very important, that creates a demand for deposit holdings that pay no interest. In some sense it is the fundamental reason why we have money, because we can think of credit constraints as a special case of search costs. The financial sector needs very few reserves, but the non-financial sector needs a lot of deposits. However, you cannot force the non-financial sector to hold more deposits than they need, as each deposit is effectively a gift of interest to a bank -- that is the bank's seignorage income. Once households have a sufficient buffer of deposits, they start to prefer the interest bearing instrument as the pool of seignorage income is finite.

Another way to think about quantitative easing specifically and things like large reserve requirements generally is that it crowds the banking system out of seignorage income as that income is diverted to the government (the central bank collects the interest payments on bonds it holds, but then sends that interest income back to treasury).

I think you have to view money through the lens of credit constraints.

[Nick Rowe]

rsj: "And again, I don't understand why people who understand Ricardian equivalence perfectly well -- whether they agree with it or not -- don't seem to understand that the private financial sector can undo any portfolio shifts of the central bank, just as the non-financial sector is capable, in principle, of undoing fiscal shifts by Treasury."

If Ricardian Equivalence is true, then any change in government saving/dissaving (holding G constant) will be exactly offset by private dissaving/saving, and so it will not affect interest rates (or anything else).

If something similar were true for monetary policy, then any change in central bank monetary tightening/loosening would be exactly offset by private money loosening/tightening, and so it will not affect interest rates (or anything else). But that conclusion is empirically false. The Bank of Canada has used monetary policy to keep inflation on target.

Asymmetric redeemability is the reason why it is false, as I have explained before.